Ion channels are proteins with a hole down their middle that allow ions to move across otherwise impermeable cell membranes, thereby controlling many important physiological functions, such as conducting electrical signals down nerve fibres and initiating muscle contraction.

We look at mathematical models describing the ion transport process through membrane channels. One important class of models is based on the Poisson-Nernst-Planck equations, a set of partial differential equations. Starting from this model we derive a simplified surrogate model to approximate current-voltage relationships and furthermore investigate inverse problems related to the structure of the underlying channel. Numerical examples will be given using a one-dimensional approximation of the system.